Knowledge of the motion parameters of a logging tool relative to a borehole is important for obtaining accurate downhole measurement signals. Thus, for example, a shift in the sensitive volume of the logging tool caused by lateral motion of the tool relative to the borehole can distort the received signal and produce inaccurate measurements. Such distortions can be especially problematic in logging-while-drilling (LWD) and measurement-while-drilling (MWD) environments, where the tool itself is subjected to severe vibration. In some cases, the measurements may have to be completely discarded, as for example when a stick-slip condition occurs (where the drill bit stops rotating momentarily because of high friction and then rapidly accelerates when the moment exerted by the drill pipe exceeds the static friction). Clearly, it would be beneficial if the tool operator had access to information about the motions of the tool, so that measurements made during strong lateral and axial motions are discarded, or not even initiated.
Additionally, in many cases, it is important to select optimal activation times for the logging measurement and, if possible, to enable correction of the received signal based on the motion parameters of the logging tool. In such applications, it is necessary to accurately determine the lateral tool velocity of the tool in real time.
In the simplest system for measuring the lateral tool velocity relative to a borehole, two mutually orthogonal accelerometers can be placed on the tool axis, such that they are sensitive to the lateral acceleration. However, such placement is generally not possible in downhole tools because of design constraints, in particular owing to the need to have an open space within the center of the tool for a mud flow channel.
As such, in prior art systems for determining the lateral velocity of a drilling tool, two pairs of accelerometers are attached to diametrically opposite sides of the tool, usually near the surface of the tool. See, for example, co-pending U.S. Pat. No. 6,268,726, assigned to the assignee of the present application. This application is incorporated herein by reference for all purposes. The accelerometers together provide radial acceleration components, ar1 and ar2, and tangential acceleration components, at1 and at2, of the tool. Since the accelerometers rotate with the tool, their measurements are in the reference frame of the rotating tool, i.e., the rotating frame. Given their opposite placement, the accelerometer pairs register equal but opposite accelerations due to lateral tool motion and equal radial (centrifugal) as well as angular accelerations due to tool rotation. The radial and tangential forces due to tool rotation are compensated for the opposite accelerations by subtracting the reading of one accelerometer from the reading of the diametrically opposite one (ar2 is subtracted from ar1 and at2 is subtracted from at1). The remaining signal is twice the actual lateral tool acceleration in the directions of ar1 and at1, respectively, as seen in the rotating frame. The acceleration components compensated for the centrifugal and angular accelerations are therefore given by the expressions:ar=(ar1−ar2)/2, for the radial tool acceleration; andat=(at1−at2)/2, for the tangential tool acceleration.
The lateral velocity is calculated by integrating the above acceleration components. There are two main problems associated with this prior art approach. First, the signal measured by the accelerometers will also contain a gravitational component if the tool orientation is not vertical. The magnitude of the gravitational component is Gsinα, where α is the angle of tool inclination relative to vertical and G is the gravitational acceleration constant. The frequency of the gravitational component is related to the tool rotation. Tool tilt away from vertical is sensed by the accelerometers and, thus, introduces an inaccuracy in the lateral tool acceleration readings.
Commonly, the gravitational acceleration component is removed from the signal by employing a high pass filter. The filter cut-off frequency is set to separate frequencies of the gravitational component modulated by the tool's rotation from the higher frequencies assumed to be caused by the tool's lateral motion. This technique, however, is not effective if the tool's rotational rate is high or not constant, for example, in a stick-slip situation, gravitational acceleration components are generated within the band of those related to the tool's lateral motion.
The second problem occurs because the accelerometers, which are placed on the tool, measure the tool's lateral velocity in the tool frame of reference rather than the desired borehole frame of reference.
With reference to FIG. 1B, while the motion parameters ar and ar are provided in the rotating reference frame, it is desirable to determine the corresponding motion parameters of the tool in the borehole reference frame XYZ. It will be appreciated that if the tool does not rotate, then the tool-reference parameters ar and at are equivalent to the borehole reference parameters ax and ay, and no conversion is necessary. If, however, the tool rotates, then ar and at are different than ax and ay, and conversion to the borehole frame of reference will be required. Similarly, it will be necessary to convert velocity components vr and vt to vx and vy, corresponding to the borehole reference frame.
Obtaining accurate lateral tool velocity is important to ensure that the accuracy of NMR porosity measurements does not degrade by more than about 5%. For example, the lateral displacement of the tool's center of gravity should be limited to about 0.1 mm relative to the borehole within a measuring time frame of 500 μseconds. In practice, it is desirable that the lateral tool velocity should not exceed 0.2 m/sec during a typical NMR reading. Tool displacements greater than about 0.25 mm may introduce a system error associated with phase shift of the NMR echo. In addition to systemic error, the signal-to-noise may also degrade.
Therefore, there is a need to provide a system and method for accurately determining the lateral tool velocity and overcoming the deficiencies associated with the prior art. By knowing the tool's velocity, the NMR signal may be corrected. Additionally, along with velocity information, an uncertainty estimator can be calculated to provide confidence levels of the measurements.